Math(s), Philosophy, History is an online reading group run by the Free Computing Lab. We read texts at the interface of mathematics, philosophy, and history. See our focus for more info.
We meet on an approximately bi-weekly basis during the academic semester. This summer (2026) we are meeting on Mondays at 12pm-1.15pm EST.
To join our mailing list, please email maths@ohrg.org with the subject header ‘JOIN’, and a 1-2 sentence explanation of your interest in the group.
As computer science has grown in stature as a discipline in the university, as Moore’s law is pushing computing into all the corners of our life and thought, there is no better time to ask why a more robust rapport between mathematics and critical theory has not emerged. Is it as simple as the fact that, as Sarah Pourciau seems to suggest, humanistic thought is aligned with the apeiron, whereas the sciences by definition rely on ‘carving’ it up into peras Pourciau - On the Digital Ocean? Or is there an interdisciplinary space where one can test the waters of a common language? We are not imagining an transdisciplinary metalanguage which is so general that noone understands anything at all, but rather a space where thought can actually happen. Can mathematics serve as the ferryman to an epistemological place where disciplinary distinctions become water under the bridge?
More specifically, our readings are designed to help us wrap our heads around the history of modern mathematics. We take modern mathematics to mean the kind that influenced the amorphous era we currently call modernity, an era which bears a relation to capitalism, but is not (we don’t think) reducible to it. (In this characterization we follow the work of Mehrtens - Moderne Sprache, Mathematik: Eine Geschichte des Streits um die Grundlagen der Disziplin und des Subjekts formaler Systeme; Siegert - Passage des Digitalen; Gray - Plato's Ghost: The Modernist Transformation of Mathematics; Hörl - Sacred Channels: The Archaic Illusion of Communication; Steingart - Axiomatics: Mathematical Thought and High Modernism.) Modernity has been understood as the attempt to be sure of ourselves without any external guarantee, such as God or a feudal order, and as such is broadly related to secular humanism Ruda - Indifference and Repetition: Or, Modern Freedom and Its Discontents. Our group is interested in charting and hypothesizing whether the insights of modern mathematics have anything to do with this modernity, whether set theory represents anything significant in the history of philosophy.
This brand of secular humanism is significant and resonant in contemporary discussions about ‘ethical computer science’, or computing for the social good—as these debates (typically) do not hinge upon explicitly religious notions of morality or social determination, but rather point themselves towards an ambiguously modern notion of freedom and the construction of a society that optimizes for this notion.
Gray - Poincaré and Counter-Modernism and Poincaré - The Foundations of Science: Science and Hypothesis, the Value of Science, Science and Method
Authors: Jeremy Gray, Henri Poincaré
Deringer - Introduction: Political Calculations
Authors: William Deringer
Bernoulli and Bernoulli - Hydrodynamics, by Daniel Bernoulli & Hydraulics, by Johann Bernoulli
Authors: Daniel Bernoulli, Johann Bernoulli
Authors: Domenico Meli
Atiyah - Mathematics in the 20th Century
Authors: Michael Atiyah
Henkle - On the Ontology of Number, or the Limits of Structuralism
Authors: Jonah Henkle
Avigad - Mathematicians in the Age of AI
Authors: Jeremy Avigad
Benacerraf - What Numbers Could Not Be
Authors: Paul Benacerraf
Husserl - The Origin of Geometry
Authors: Edmund Husserl
Longo - The Constructed Objectivity of Mathematics and the Cognitive Subject
Authors: Giuseppe Longo
Von Foerster - Understanding Understanding: Essays on Cybernetics and Cognition, pp.1-20, 247-261
Authors: Heinz Von Foerster
Naderi - Mark and Lack: Formalism as Fidelity
Authors: Reza Naderi
Miller - Suture (Elements of the Logic of the Signifier)
Authors: Jacques Miller
Schmid - Diagonal Method and Dialectical Logic: Book Two Revisited
Authors: Eric Schmid
Authors: Michael Castelle
Weatherby - Language Machines: Cultural AI and the End of Remainder Humanism, pp.1-40
Authors: Leif Weatherby
Mehrtens - Nationalism and Internationalism
Authors: Herbert Mehrtens
Authors: George Berkeley
Mazzotti - Reactionary Mathematics: A Genealogy of Purity, pp.128-146
Authors: Massimo Mazzotti
Steingart - Axiomatics: Mathematical Thought and High Modernism, pp.1-24
Authors: Alma Steingart
Marx - The Myth of the Martians and the Golden Age of Hungarian Science
Authors: George Marx
Rodin - Categorial Logic and Hegelian Dialectics
Authors: Andrei Rodin
Warwick - Masters of Theory: Cambridge and the Rise of Mathematical Physics, pp.ix-xi, 212-226
Authors: Andrew Warwick
Marx - Mathematical Manuscripts of Karl Marx, pp.109-119
Authors: Karl Marx
Vasiliev - Imaginary (Non-Aristotelian) Logic
Authors: N. A. Vasiliev
Krieger - Convention: How Means and Variances Are Entrenched as Statistics
Authors: Martin Krieger
Hörl - Sacred Channels: The Archaic Illusion of Communication, pp.89-108
Authors: Erich Hörl
Authors: Michel Serres
Joque - Revolutionary Mathematics: Artificial Intelligence, Statistics and the Logic of Capitalism
Authors: Justin Joque
Babbage - On the Economy of Machinery and Manufactures, pp.i-50
Authors: Charles Babbage
Peirce - Elements of Logic, pp.134-173
Authors: Charles Peirce
Turing - Intelligent Machinery, A Heretical Theory (c.1951) and Turing - Can Digital Computers Think? (1951)
Authors: Alan Turing
Gray - Plato's Ghost: The Modernist Transformation of Mathematics, pp.18-38
Authors: Jeremy Gray
Von Neumann - The Mathematician
Authors: John von Neumann
Thurston - On Proof and Progress in Mathematics
Authors: William P. Thurston
Aaronson - Why Philosophers Should Care about Computational Complexity
Authors: Scott Aaronson
Pourciau - A/Logos: An Anomalous Episode in the History of Number and Pourciau - On the Digital Ocean
Authors: Sarah Pourciau